Page 37 - Design and Operation of Heat Exchangers and their Networks

24 Design and operation of heat exchangers and their networks

1=3
h i 3 h i 3
3 1=3 1=2 1=6
ð
Nu x,H ¼ 4:354 +1:302 RePrd i =xÞ 1 +0:462 RePrd i =xÞ Pr
ð
1=3
h i 3 h i 3
3
¼ 4:354 +1:302 34:54 1=3 1 +0:462 34:54 1=2 0:7047 1=6
¼ 5:198
Nu x,H λ 5:198 0:0281
2
α x,H ¼ ¼ ¼ 6:954 W=m K
d i 0:021
By considering 5% uncertainty in α x,H , the overall heat transfer
coefficient between the tube outside surface and the air flow at x¼L is
1
1 ln d o =d i Þ
ð
k ¼ + d i
ð 1 0:05Þα H 2λ w
1
1 ln 0:025=0:021Þ 2
ð
¼ +0:021 ¼ 6:601W=m K
ð 1 0:05Þ 6:954 2 15
from which we obtain the length of the heating section by
Q 26:07
L ¼ ¼ ¼ 0:4989 m
πd i kΔt π 0:021 6:601 120
Using the newly calculated length and repeating the earlier calculations,
we finally obtain L¼ 0.4822m. That means that the heating section length
should not be shorter than 0.4822m, and L¼0.5m is recommended.
The detailed calculation can be found in the MatLab code for Example
2.2 in the appendix.

2.1.1.4 Laminar flow between parallel plates
For fully developed laminar flow between parallel plates with the same con-
stant wall temperature, the Nusselt number is a constant:

Nu T ¼ 7:5407 (2.24)
For fully developed laminar flow between parallel plates with constant
but different heat flux at each wall, the Nusselt number are obtained as
(Shah and London, 1978)
140
Nu H,p1 ¼ (2.25)
26 9q p2 =q p1
where p1 denotes one plate wall and p2 the other.